Heat generation point detection method and heat generation point detection device

ABSTRACT

A heat generation point detection method comprises steps S 01 , S 02  of applying a low frequency bias voltage to an integrated circuit S and acquiring a heat generation detection signal detected from the integrated circuit S in response thereto, steps S 03 , S 04  of supplying a high frequency bias voltage to the integrated circuit S and acquiring a heat generation detection signal detected from the integrated circuit S in response thereto, steps S 05  to S 07  of detecting a phase shift between the low frequency bias voltage and the heat generation detection signal and a phase shift between the high frequency bias voltage and the heat generation detection signal, and a step S 08  of calculating a change rate of the phase shift against a square root of the frequency of the bias voltage, based on those phase shifts, and acquiring depth information of a heat generation point from the change rate.

This is a continuation application of copending application Ser. No.14/232,021, having a § 371 date of Feb. 4, 2014, which is a nationalstage filing based on PCT International Application No.PCT/JP2012/067706, filed on Jul. 11, 2012. The copending applicationSer. No. 14/232,021 is incorporated by reference herein in its entirety.

TECHNICAL FIELD

The present invention relates to a heat generation point detectionmethod and a heat generation point detection device for detecting adepth of a heat generation point in an integrated circuit.

BACKGROUND ART

A method of applying a periodic pulse voltage to an integrated circuitand detecting a thermal response is known as a conventional failureanalysis method for integrated circuits such as LSI packages. Forexample, Non Patent Literature 1 below describes that a phase shift ΔΦbetween electrical excitation and a local thermal response is detectedand a depth of a defect is determined from the phase shift ΔΦ.

CITATION LIST Non Patent Literature

-   Non Patent Literature 1: C. Schmidt et al., “Lock-in-Thermography    for 3-dimensional localization of electrical defects inside complex    packaged devices,” ISTFA2008: Proceedings from the 34th    International Symposium for Testing and Failure Analysis, U.S.A.,    November 2008, p. 102-107.

SUMMARY OF INVENTION Technical Problem

In the above-described conventional analysis method, however, the phaseshift ΔΦ is dependent on an amount of heat generation, a structure of anintegrated circuit, and a position of a defect point, as well as thedepth of the defect point because the amount of heat generation variesdepending upon the amplitude of an excitation signal and the conditionof the defect point and because the heat capacity between the defectpoint and the surface of the integrated circuit varies depending uponthe position of the defect point. Therefore, when the depth of thedefect was evaluated from the phase shift ΔΦ, an error of an evaluatedvalue thereof tended to become larger.

Under such circumstances, the present invention has been accomplished inview of the foregoing problem and it is an object of the presentinvention to provide a heat generation point detection method and a heatgeneration point detection device allowing accurate detection of a depthof a heat generation point in an integrated circuit, independent of thecondition and position thereof.

Solution to Problem

In order to solve the above problem, a heat generation point detectionmethod according to an aspect of the present invention is a heatgeneration point detection method for detecting a depth of a heatgeneration point in an integrated circuit, comprising: a first step ofsupplying a periodic electric signal fluctuating at a first frequency,to the integrated circuit and acquiring a first detection signalindicative of a change of an amount of heat generation detected from theintegrated circuit in response thereto; a second step of supplying aperiodic electric signal fluctuating at a second frequency differentfrom the first frequency, to the integrated circuit and acquiring asecond detection signal indicative of a change of an amount of heatgeneration detected from the integrated circuit in response thereto; athird step of detecting a first phase shift between the periodicelectric signal of the first frequency and the first detection signaland a second phase shift between the periodic electric signal of thesecond frequency and the second detection signal; and a fourth step ofcalculating a change rate of the phase shift between the periodicelectric signal and the detection signal against a variable calculatedfrom the frequency of the periodic electric signal, based on the firstand second phase shifts, and acquiring depth information of the heatgeneration point from the change rate.

Furthermore, a heat generation point detection device according toanother aspect of the present invention is a heat generation pointdetection device for detecting a depth of a heat generation point in anintegrated circuit, comprising: an electric signal supply unit forsupplying an electric signal to the integrated circuit; a control unitfor controlling the electric signal supply unit so as to supply aperiodic electric signal fluctuating at a first frequency and a periodicelectric signal fluctuating at a second frequency different from thefirst frequency, to the integrated circuit; a detection unit foracquiring a first detection signal indicative of a change of an amountof heat generation detected from the integrated circuit in response tosupply of the periodic electric signal of the first frequency andacquiring a second detection signal indicative of a change of an amountof heat generation detected from the integrated circuit in response tosupply of the periodic electric signal of the second frequency; a phaseshift detection unit for detecting a first phase shift between theperiodic electric signal of the first frequency and the first detectionsignal and a second phase shift between the periodic electric signal ofthe second frequency and the second detection signal; and a calculationunit for calculating a change rate of the phase shift between theperiodic electric signal and the detection signal against a variablecalculated from the frequency of the periodic electric signal, based onthe first and second phase shifts, and acquiring depth information ofthe heat generation point from the change rate.

The heat generation point detection method or the heat generation pointdetection device is configured to detect the first detection signalindicative of the change of the amount of heat generation in response tothe supply of the periodic electric signal of the first frequency anddetect the second detection signal indicative of the change of theamount of heat generation in response to the supply of the periodicelectric signal of the second frequency, from the integrated circuit.Then the first phase shift between the periodic electric signal of thefirst frequency and the first detection signal and the second phaseshift between the periodic electric signal of the second frequency andthe second detection signal are detected and the depth information ofthe heat generation point is obtained from the change rate of the phaseshift against the variable calculated from the frequency of the periodicelectric signal. This procedure is to calculate the depth informationwhile cancelling out an offset component in the temporal change of theamount of heat generation varying depending upon the position of theheat generation point; therefore, the depth information is obtained withhigh accuracy, independent of the position of the heat generation point.By acquiring the change rate of the phase shift against the variablecalculated from the frequency of the periodic electric signal, we canalso obtain the depth information independent of the amount of heatgeneration at the heat generation point, the internal structure of theintegrated circuit, and the frequency of the periodic electric signal.

Advantageous Effect of Invention

The present invention allows accurate detection of the depth of the heatgeneration point in the integrated circuit, independent of the conditionand position thereof.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a block diagram showing a schematic configuration of anintegrated circuit failure analysis device according to a preferredembodiment of the present invention.

FIG. 2 is a flowchart showing a procedure of a failure analysisoperation for an integrated circuit S by the integrated circuit failureanalysis device 1 in FIG. 1.

FIG. 3 is a drawing showing a temporal change of bias voltages appliedby a voltage application unit 14 in FIG. 1.

FIG. 4 is a drawing wherein (a) shows a temporal change of a biasvoltage, (b) a temporal change of a heat generation detection signaldetected in an integrated circuit S comprised of a material with lowheat capacity/low heat transfer coefficient, and (c) a temporal changeof a heat generation detection signal detected in an integrated circuitS comprised of a material with high heat capacity/high heat transfercoefficient.

FIG. 5 is a drawing wherein (a) shows a temporal change of a biasvoltage applied at a low frequency, (b) a temporal change of a heatgeneration detection signal detected in the integrated circuit S, (c) atemporal change of a bias voltage applied at a high frequency, and (d) atemporal change of a heat generation detection signal detected in theintegrated circuit S.

FIG. 6 is a graph showing a relationship between a square root ofangular frequency of bias voltages applied to the integrated circuit Sand observed phase delay bx, in the integrated circuit failure analysisdevice in FIG. 1.

DESCRIPTION OF EMBODIMENTS

The preferred embodiments of the heat generation point detection deviceaccording to the present invention and the heat generation pointdetection method using the same will be described below in detail withreference to the drawings. Identical or equivalent portions will bedenoted by the same reference signs in the description of the drawings,without redundant description.

FIG. 1 is a block diagram showing a schematic configuration of anintegrated circuit failure analysis device which is a heat generationpoint detection device according to a preferred embodiment of thepresent invention. The integrated circuit failure analysis device 1shown in the same drawing is a failure analysis device which detects aposition of a heat generation point in an integrated circuit S such asan LSI package and performs a failure analysis. This integrated circuitfailure analysis device 1 is configured with a sample stage 10, a stagedrive unit 12 to drive the sample stage 10, a voltage application unit(electric signal supply unit) 14, an imaging device 18, a control unit20, and an image processing unit 30.

The integrated circuit S as an analysis target is mounted on the samplestage 10 using X-, Y-, and Z-stages which can be driven in X-axisdirection, Y-axis direction (horizontal direction), and Z-axis direction(vertical direction), respectively. This sample stage 10 is configuredso that it can be driven in the X-, Y-, and Z-directions by the stagedrive unit 12, thereby to carry out focusing in imaging, positionalignment of imaging position, and so on for the integrated circuit S.The imaging device 18 as imaging means for acquiring a two-dimensionalimage of the integrated circuit S is installed above the sample stage10. The imaging device 18 to be suitably used herein is an imagingdevice sensitive to a predetermined wavelength region, for acquiring animage based on a heat generation image on the surface of the integratedcircuit S, e.g., an infrared imaging device sensitive to the infraredwavelength region.

A light-guide optical system 16 such as an objective lens for guidingthe image on the surface of the integrated circuit S to the imagingdevice 18 is disposed on the optical axis between the sample stage 10and the imaging device 18. The integrated circuit failure analysisdevice may be configured as follows: the light-guide optical system 16is provided with a driving mechanism such as X-, Y-, and Z-stages andthis driving mechanism allows the device to implement the focusing inimaging, the position alignment of imaging position, and so on for theintegrated circuit S.

The integrated circuit failure analysis device is provided with thevoltage application unit 14 for supplying a voltage signal to theintegrated circuit S on the sample stage 10. The voltage applicationunit 14 is voltage application means for applying a necessary biasvoltage to an electronic circuit in the integrated circuit S in carryingout a failure analysis based on detection of a heat generation point,and is configured including a power supply for application of voltage.Specifically, the voltage application unit 14 applies a voltage signal(periodic electric signal) of a rectangular wave fluctuatingperiodically, as a bias voltage. This operation results in applying ahigh voltage and a low voltage periodically to the integrated circuit S.The voltage application unit 14 is configured so that the frequency(repetition period) of the applied bias voltage can be changed bycontrol of the control unit 20. The voltage application unit 14 isconfigured so that values of the high voltage and low voltage of theapplied bias voltage can be changed by control of the control unit 20.

The imaging device 18 acquires a plurality of analysis images in timeseries in a state in which the bias voltage is applied to the integratedcircuit S by the voltage application unit 14. The analysis imagesacquired in this manner are images including the heat generation imageon the surface of the integrated circuit S. The imaging frequency (framerate) of the imaging device 18 may be set based on the frequency of thebias voltage applied to the integrated circuit S by the voltageapplication unit 14. For example, the imaging frequency of the imagingdevice 18 may be the same period as the frequency of the bias voltageapplied to the integrated circuit S or may be set in proportion to thefrequency of the bias voltage. This setting allows the device to acquireheat generation images in relatively identical heat generationconditions, even at different frequencies of bias voltages.

Furthermore, for these sample stage 10, stage drive unit 12, voltageapplication unit 14, light-guide optical system 16, and imaging device18, the integrated circuit failure analysis device 1 is provided with acontrol unit 20 for controlling operations thereof. This control unit 20is configured with an imaging control unit 21, a stage control unit 22,and a synchronism control unit 23.

The imaging control unit 21 controls the bias voltage applicationoperation by the voltage application unit 14 and the image acquisitionoperation by the imaging device 18, thereby to control the acquisitionof analysis images of the integrated circuit S. The stage control unit22 controls the operation of the sample stage 10 and the stage driveunit 12 (the moving operation of the integrated circuit S on the samplestage 10). The synchronism control unit 23 performs a control forachieving necessary synchronism of the imaging control unit 21 and thestage control unit 22 with the image processing unit 30 provided for theimaging device 18. Namely, the synchronism control unit 23 controls thestage control unit 22 to move the stage to a predetermined position forexecution of a failure analysis of the integrated circuit S andthereafter controls the imaging control unit 21 to change frequencies ofbias voltages at predetermined intervals in order. The synchronismcontrol unit 23 also controls the value of the high voltage and thevalue of the low voltage in the bias voltage applied periodically. Thesynchronism control unit 23 controls the imaging control unit 21 toseparately acquire the analysis images of the integrated circuit S intime with change timings of the frequencies of the bias voltages.

The image processing unit 30 is image processing means for performingimage processing necessary for the failure analysis of the integratedcircuit S, on the images acquired by the imaging device 18. The imageprocessing unit 30 in the present embodiment is configured with an imagestorage unit 31, a heat generation signal acquisition unit (detectionunit) 32, a voltage phase acquisition unit 33, a phase delay acquisitionunit (phase shift detection unit) 34, and a depth informationcalculation unit 35. The images of the integrated circuit S acquired bythe imaging device 18 are fed to the image processing unit 30 and storedand accumulated in the image storage unit 31 as occasion may demand.

The heat generation signal acquisition unit 32 acquires a heatgeneration detection signal indicative of a temporal change of an amountof heat generation detected at a plurality of points on the surface ofthe integrated circuit S, based on the plurality of analysis imagesacquired in time series.

The voltage phase acquisition unit 33 receives the waveform of the biasvoltage applied by the voltage application unit 14, from the synchronismcontrol unit 23, and acquires information of the phase of the biasvoltage. The information of the phase of the bias voltage may beacquired by the voltage application unit 14 or by the control unit 20and then supplied to the voltage phase acquisition unit 33 therefrom.

The phase delay acquisition unit 34 acquires information of the phase ofa heat generation detection signal with respect to the information ofthe phase of the bias voltage applied by the voltage application unit14, based on the heat generation detection signal indicative of thetemporal change of the amount of heat generation acquired by the heatgeneration signal acquisition unit 32 and the phase information acquiredby the voltage phase acquisition unit 33. This information of the phaseof the heat generation detection signal corresponds to a phase shiftbetween the bias voltage and the heat generation detection signaldetected upon application of the bias voltage and, specifically, thephase delay acquisition unit 34 calculates a difference between thephase of the heat generation detection signal acquired by the heatgeneration signal acquisition unit 32 and the phase information acquiredby the voltage phase acquisition unit 33. Here, the phase delayacquisition unit 34 detects the phase shift between the bias voltage andthe heat generation detection signal, for each of the bias voltageschanged to a plurality of frequencies. The phase delay acquisition unit34 may directly acquire the phase shift by lock-in processing, fromobjects of the waveform of the heat generation detection signal and thewaveform of the bias voltage. In this case, an output signal about thephase shift can be acquired by feeding the heat generation detectionsignal and the bias signal to a lock-in detector.

The depth information calculation unit 35 calculates the depthinformation of the heat generation point in the integrated circuit S,based on a plurality of phase shifts corresponding to the bias voltagesof a plurality of frequencies, which were detected by the phase delayacquisition unit 34. Namely, the depth information calculation unit 35calculates a change rate of the phase shift against a square root of thefrequency which is a variable calculated from the frequency of the biasvoltage, and calculates as the depth information the change rate or avalue obtained by multiplying the change rate by a predeterminedconstant. This predetermined constant is preliminarily set as acoefficient about heat transfer dependent on physical properties of amaterial of the integrated circuit S. The depth information calculatedin this manner indicates the depth of the heat generation point detectedover a plurality of points in the integrated circuit S and is used forthe failure analysis of the integrated circuit S.

The image processing unit 30 of this configuration is constructed, forexample, using a computer. An input device 36 and a display device 37are connected to this image processing unit 30. The input device 36 iscomposed, for example, of a keyboard, a mouse, and so on and is used,for example, to enter information and operation instructions necessaryfor execution of the image acquisition operation and the failureanalysis operation in the integrated circuit failure analysis device 1.The display device 37 is composed, for example, of a CRT display, aliquid crystal display, or the like and is used, for example, to displayvarious kinds of information such as the images and the depthinformation about the failure analysis in the integrated circuit failureanalysis device 1.

This image processing unit 30 may be configured so that it, togetherwith the control unit 20, is implemented as a single control device(e.g., a single computer). Concerning the input device 36 and thedisplay device 37 connected to the image processing unit 30, they mayalso be configured similarly so as to function as input device anddisplay device connected not only to the image processing unit 30 butalso to the control unit 20.

The following will describe the procedure of the failure analysisoperation about the integrated circuit S by the integrated circuitfailure analysis device 1 and detail the heat generation point detectionmethod according to the present embodiment. FIG. 2 is a flowchartshowing the procedure of the failure analysis operation about theintegrated circuit S by the integrated circuit failure analysis device1, and FIGS. 3 to 5 are drawings showing temporal changes of signalwaveforms processed in the failure analysis operation by the integratedcircuit failure analysis device 1.

First, the synchronism control unit 23 controls the voltage applicationunit 14 to apply a bias voltage fluctuating at a low frequency (e.g., 1Hz), to the integrated circuit S (step S01). This control causes a highvoltage and a low voltage to be applied periodically to the integratedcircuit S. In conjunction therewith, the imaging control unit 21controls the imaging device 18 to separately acquire images according tothe application timing of the low-frequency bias voltage. For example,the imaging control unit 21 controls the imaging device 18 to takeimages at the same frequency as the low frequency applied to theintegrated circuit S or at an imaging frequency (frame rate)proportional to the low frequency. The images of the integrated circuitS acquired in this manner are stored once into the image storage unit 31and thereafter processed by the heat generation signal acquisition unit32, thereby to acquire a heat generation detection signal indicative ofa temporal change of an amount of heat generation at a plurality ofpoints (step S02).

Next, the synchronism control unit 23 controls the voltage applicationunit 14 to apply a bias voltage fluctuating at a high frequency (e.g., 2Hz), to the integrated circuit S (step S03). This control causes a highvoltage and a low voltage to be applied periodically to the integratedcircuit S. In conjunction therewith, the imaging control unit 21controls the imaging device 18 to separately acquire images according tothe application timing of the high-frequency bias voltage. For example,the imaging control unit 21 controls the imaging device 18 to takeimages at the same frequency as the high frequency applied to theintegrated circuit S or at an imaging frequency (frame rate)proportional to the high frequency. The images of the integrated circuitS acquired in this manner are stored once into the image storage unit 31and thereafter processed by the heat generation signal acquisition unit32, thereby to acquire a heat generation detection signal at a pluralityof points (step S04). The frequencies of the bias voltages applied insteps S01, S03 may be suitably changed but are preferably set to notmore than 10 Hz because too high frequencies must lead to placedependency of heat transference and amount of heat generation. Thefrequencies of the bias voltages changed do not always have to belimited to two types, but may be three or more types to acquire heatgeneration detection signals according thereto.

FIG. 3 shows a temporal change of the bias voltages applied in stepsS01, S03. As shown in the same drawing, the synchronism control unit 23controls the bias voltages so that a high-frequency period P2 follows alow-frequency period P1 in series and, a duration of acquisition of theheat generation detection signal in each of the period P1 and the periodP2 is set so that a certain length of time passes after a start ofapplication of the bias voltage in each of the periods P1, P2, in orderto make the temperature in the integrated circuit S constant betweenthose durations so as not to affect the amount of heat generation. It isalso permissible to place a period without application of voltagebetween the period P1 and the period P2. The maximum voltages V₁ andminimum voltages V₂ of the bias voltages of rectangular waves are set atrespective identical values between the frequencies so as to equalizeconditions during heat generation in the integrated circuit S and theduty ratios of the bias voltages are also set at an identical value(e.g., 50%, 75%, . . . ) between the frequencies so as to equalizeamounts of heat generation in the integrated circuit S. This is forkeeping an average temperature of a sample constant by making the amountof heat generation constant in the integrated circuit S. In this case,it is also possible to set the durations of acquisition of heatgeneration detection signals in the period P1 and in the period P2continuous.

Referring back to FIG. 2, from targets of the waveforms of thelow-frequency and high-frequency bias voltages applied to the integratedcircuit S in steps S01, 03, the voltage phase acquisition unit 33 thenacquires the phase information thereof (step S05).

Next, from processing targets of the heat generation detection signalscorresponding to the application of the low-frequency and high-frequencybias voltages, which were acquired in steps S02, S04, the phase delayacquisition unit 34 acquires the phase information thereof with respectto the information of the phases of the bias voltages acquired in stepS05 and detects phase shifts of the respective heat generation detectionsignals (steps S06, S07). Specifically, the phase delay acquisition unit34 detects the phase shift from the heat generation detection signalabout each of the low-frequency and high-frequency bias voltages, basedon the heat generation detection signals corresponding to theapplication of the low-frequency and high-frequency bias voltages, whichwere acquired in steps S02, S04, and based on the information of thephases of the waveforms of the low-frequency and high-frequency biasvoltages applied to the integrated circuit S in steps S01, 03. Next, thedepth information calculation unit 35 calculates a change rate of thephase shift against the square root of the frequency, based on the phaseshifts corresponding to the two frequencies, and multiplies the changerate by a predetermined constant to obtain the depth information (stepS08). This depth information is calculated over a plurality of points onthe surface of the integrated circuit S. Finally, the depth informationthus calculated is processed as failure analysis information anddisplayed on the display device 37 (step S09).

The below will describe a mechanism of detection of the depthinformation of a heat generation point by the integrated circuit failureanalysis device 1.

In FIG. 4, (a) shows a temporal change of a bias voltage applied at acertain frequency, (b) a temporal change of a heat generation detectionsignal detected in the integrated circuit S comprised of a material withlow heat capacity/low heat transfer coefficient in response thereto, and(c) a temporal change of a heat generation detection signal detected inthe integrated circuit S comprised of a material with high heatcapacity/high heat transfer coefficient in response thereto. A phaseshift calculated by the phase delay acquisition unit 34 in theintegrated circuit failure analysis device 1 is D1 and this phase shiftD1 includes a phase shift component D2 determined by a depth of a heatgeneration point in the integrated circuit S and a phase shift componentD3 due to differences of delay of heat generation, heat capacity, andheat transfer rate. The shift component D3 in the phase shift D1 issignificantly affected by a material of a heat transfer path in theintegrated circuit S.

This difference of the phase shift D1 depending on the material can beexplained as follows. A quantity Q of heat one-dimensionally transferredfrom the interior of the integrated circuit S is represented byExpression (1) below;[Math 1]Q=1+exp{−ax+i(wt−bx)}  (1)

In this expression, x represents a distance from a heat generationsource to an observation point (surface) (=depth of the heat generationpoint), Q a quantity of heat passing the observation point, w theangular frequency (½π Hz), b a phase delay per unit length, and a anattenuation rate per unit length. A temperature T against this heatquantity Q is represented as changing quantity by Expression (2) below;

$\begin{matrix}\left\lbrack {{Math}\mspace{14mu} 2} \right\rbrack & \; \\{{{d\; T} = {{- \frac{1}{\rho\; q}}\frac{dQ}{dx}}},} & (2)\end{matrix}$where q represents the specific heat and ρ the density.

Furthermore, from the thermal diffusion equation, where the heattransfer coefficient is denoted by κ, Expression (3) below is derived;

$\begin{matrix}\left\lbrack {{Math}\mspace{14mu} 3} \right\rbrack & \; \\{\frac{dQ}{dt} = {{i\;{w\left( {Q - 1} \right)}} = {\kappa{\frac{d^{2}T}{{dx}^{2}}.}}}} & (3)\end{matrix}$From Expressions (2) and (3), Expression (4) below is derived.

$\begin{matrix}\left\lbrack {{Math}\mspace{14mu} 4} \right\rbrack & \; \\{{Q - 1} = {{- {i\left( \frac{\kappa}{w\;\rho\; q} \right)}}\frac{d^{2}Q}{{dx}^{2}}}} & (4)\end{matrix}$The second derivative of Q with respect to x is derived from Expression(1), to obtain Expression (5) below;

$\begin{matrix}\left\lbrack {{Math}\mspace{14mu} 5} \right\rbrack & \; \\{{\frac{d^{2}Q}{{dx}^{2}} = {\left( {a + {i\; b}} \right)^{2}\left( {Q - 1} \right)}},} & (5)\end{matrix}$and from Expressions (4) and (5), Expression (6) below is furtherderived;

$\begin{matrix}\left\lbrack {{Math}\mspace{14mu} 6} \right\rbrack & \; \\{\left( {a + {i\; b}} \right)^{2} = {- {{i\left( \frac{w\;\rho\; q}{\kappa} \right)}.}}} & (6)\end{matrix}$Since the square root of imaginary i is (1+i)/√2, Expression (6) ismodified into Expression (7) below;

$\begin{matrix}\left\lbrack {{Math}\mspace{14mu} 7} \right\rbrack & \; \\{{a + {i\; b}} = {{\pm \frac{1 + i}{\sqrt{2}}}{\sqrt{\frac{\rho\; q\; w}{\kappa}}.}}} & (7)\end{matrix}$By expanding the above Expression (7), the attenuation constant a andthe proportionality constant b of phase delay amount are expressed asExpression (8) below;

$\begin{matrix}\left\lbrack {{Math}\mspace{14mu} 8} \right\rbrack & \; \\{a = {b = {\sqrt{\frac{\rho\; q\; w}{2\;\kappa}} = {\sqrt{f}{\sqrt{\frac{\rho\; q\;\pi}{\kappa}}.}}}}} & (8)\end{matrix}$It is, however, noted that the above relation excludes the signsindicative of opposite heat flows. As a matter of fact, the phase delayquantity can have an offset due to occurrence of distortion of waveformif there is a nonlinear factor such as transfer of heat through aplurality of paths, e.g., reflection from the sample edge, or slowerheat transfer from the surface to the atmosphere than inside the sample,in actual measurement.

The conventional technology was to consider that the phase delay bx ofheat generation observed at an observation point (surface) wasproportional to the depth, and to simply calculate the depth of the heatgeneration source, based thereon. However, the offset can be produced inthe actual delay quantity. This is dependent on the heat capacity insidethe integrated circuit S, the amount of heat generation, the shape, thefrequency of applied bias, and so on. For this reason, the phase offsetvaries depending upon where observation is conducted in the integratedcircuit S, in the conventional technology, and it is difficult to alwayscalculate an accurate depth of the heat generation source by theconventional technology. In contrast to it, the heat generation pointdetection method according to the present embodiment makes use of thefinding that, as to the heat generation detection signals from theinterior of the package of the integrated circuit S, the phase offsethas little change against the square root of the frequency, at the lowfrequencies of the applied biases of not more than several Hz. Thefrequencies applicable herein have an upper limit value varyingdepending upon the integrated circuit S and are preferably not more than4 Hz.

Namely, the depth information detected in the heat generation pointdetection method according to the present embodiment is a slope of thephase delay bx against the square root of the frequency, and is a valuerepresented by Expression (9) below;

$\begin{matrix}\left\lbrack {{Math}\mspace{14mu} 9} \right\rbrack & \; \\{\frac{dbx}{d\sqrt{f}} = {x{\sqrt{\frac{\rho\; q\;\pi}{\kappa}}.}}} & (9)\end{matrix}$This value is dependent on only the constants ρ, q, and κ determined byphysical properties, and the constant π, successfully excluding theinfluence of the phase offset.

In FIG. 5, (a) shows a temporal change of a bias voltage applied at alow frequency of 1 Hz, (b) a temporal change of a heat generationdetection signal detected in the integrated circuit S in responsethereto, (c) a temporal change of a bias voltage applied at a highfrequency of 2 Hz, and (d) a temporal change of a heat generationdetection signal detected in the integrated circuit S in responsethereto. In the integrated circuit failure analysis device 1, a delaycorresponding to the phase delay bx is observed as a delay quantity D1at each frequency. This delay quantity D1 includes a phase shiftcomponent D2 determined by a depth of a heat generation point and aphase shift component D3 determined by the shape of the interior of asample, the condition of the surface, and so on.

FIG. 6 shows a relationship between the square root of the angularfrequency w of the bias voltage applied to the integrated circuit S andthe observed phase delay bx, in the integrated circuit failure analysisdevice 1. As shown in the same drawing, each of the phase delays D1observed at the low angular frequency w₁ and at the high angularfrequency w₂ includes the shift component D2 and the shift component D3.When we calculate the slope of the phase delay bx against the squareroot of the angular frequency w, we can estimate the depth informationindependent of the heat capacity inside the integrated circuit S, theamount of heat generation, and the position, which is determined by theshift component D2 determined by the depth of the heat generation point,while eliminating the phase offset component D3.

The integrated circuit failure analysis device 1 and the heat generationpoint detection method using the same as described above includedetecting the heat generation detection signal in response to theapplication of the low-frequency bias voltage and detecting the heatgeneration detection signal in response to the application of thehigh-frequency bias voltage, from the integrated circuit S. Thendetected are the phase shift between the low-frequency bias voltage andthe heat generation detection signal and the phase shift between thehigh-frequency bias voltage and the heat generation detection signaland, the depth information of the heat generation point is obtained fromthe change rate of the phase shift against the square root of thefrequency. This procedure results in calculating the depth informationwhile cancelling out the offset component in the temporal change of theamount of heat generation varying depending upon the position of theheat generation point, whereby the depth information is obtained withhigh accuracy, independent of the position of the heat generation point.Moreover, by obtaining the change rate of the phase shift against thevariable calculated from the frequency of the bias voltage, we can alsoobtain the depth information independent of the amount of heatgeneration at the heat generation point, the internal structure of theintegrated circuit, and the frequency of the bias voltage.

Namely, the phase delay bx between the bias voltage and the heatgeneration detection signal involves deformation of the heat generationdetection waveform dependent on the quantity of heat from the heatgeneration source, the position of the heat generation point in theintegrated circuit S, the internal structure and the heat capacity ofthe integrated circuit, and so on, and thus includes variationassociated therewith. Therefore, direct evaluation of the phase delay bxleads to failure in calculating an accurate depth of the heat generationpoint. For example, even if a parameter is one allowing us to calculatean accurate depth as long as the measurement is carried out in thecenter of the integrated circuit S, a significant error is made bydirectly applying the parameter to the measurement at the sample edge.The error of this kind is made by a difference of heat transfer rate anda difference of the sum of heat capacity in a heat transferred range.Specifically, it varies as shown in FIG. 4, with increase of heatcapacity and increase of heat transfer rate. In the phase delay bx, theshift component D3 due to the deformation of the response waveform isproduced from the minimum 0° to the maximum 90°, in addition to theshift component D2 corresponding to the phase delay from the heatgeneration source. This component becomes an extra offset, which hasmade the calculation of accurate depth difficult heretofore. The presentembodiment allows us to obtain the accurate depth information whileremoving such extra offset.

Since the amplitudes and duty ratios of the bias voltages of multiplefrequencies applied to the integrated circuit S are set to be equal toeach other, the amounts of heat generation at the heat generation pointcan be made more uniform and the dependency of the depth information onthe frequency of the bias voltage can be reduced more. As a result, muchmore accurate depth information can be acquired.

The present invention is by no means limited to the above-describedembodiment. For example, the waveforms of the bias voltages applied tothe integrated circuit S do not have to be limited to the rectangularwaves, but may be other waveforms of voltages fluctuating periodically,like sinusoidal waves or triangular waves.

The maximum V₁ and minimum V₂ of the bias voltages may also be suitablychanged according to a type of the integrated circuit S. However, when aplurality of frequencies are used as changed for one integrated circuitS, it is preferable to set the maximum V₁ and minimum V₂ constant.

Since an increase or a decrease of the frequency of the bias voltageleads to variation in amplitude of the heat generation detection signal,it is necessary to keep the amplitude at the lowest frequency to bemeasured, within a measurable range. Then, the integrated circuitfailure analysis device 1 may be provided with a function toautomatically detect an event of the amplitude of the heat generationdetection signal exceeding the measurable range and output an error.

The fourth step is preferably to calculate the change rate of the phaseshift against the variable which is the square root of the frequency.This allows us to obtain higher-accuracy depth information, independentof the position of the heat generation point, the amount of heatgeneration, the internal structure of the integrated circuit, and thefrequency of the periodic electric signal.

It is also preferable that the duty ratios of the periodic electricsignals supplied in the first step and the second step be equal to eachother. In this case, the amounts of heat generation at the heatgeneration point can be made more uniform, whereby the dependency of thedepth information on the frequency of the periodic electric signal canbe reduced more.

It is preferable that the synchronism control unit 15 set and controleach of the maximum voltage V₁ and the minimum voltage V₂ of thelow-frequency and high-frequency bias voltages so that the duty ratiosin the predetermined durations of the periodic electric signals suppliedin the first step and the second step become equal to each other. Thismakes the amount of heat generation in the low-frequency bias voltageapplication period approximately equal to the amount of heat generationin the high-frequency bias voltage application period, and thus itbecomes feasible to apply the low-frequency bias voltage and thehigh-frequency bias voltage in series, with expectations of reduction ofmeasurement time and improvement in measurement accuracy.

INDUSTRIAL APPLICABILITY

The present invention is applicable to the heat generation pointdetection methods and heat generation point detection devices fordetecting the depth of the heat generation point in the integratedcircuit and allows accurate detection of the depth of the heatgeneration point in the integrated circuit, independent of the conditionand position thereof.

REFERENCE SIGNS LIST

-   -   1 integrated circuit failure analysis device; 14 voltage        application unit (electric signal supply unit); 18 imaging        device; 20 control unit; 21 imaging control unit; 22 stage        control unit; 23 synchronism control unit; 30 image processing        unit; 31 image storage unit; 32 heat generation signal        acquisition unit (detection unit); 33 voltage phase acquisition        unit; 34 phase delay acquisition unit (phase shift detection        unit); 35 depth information calculation unit; S integrated        circuit.

The invention claimed is:
 1. A method for acquiring a depth of a heatgeneration point in an integrated circuit, comprising: supplying a firstelectric signal at a first frequency to the integrated circuit;acquiring a first detection signal indicative of a change of an amountof heat generation detected from the integrated circuit in response thefirst electric signal; acquiring a first phase shift between the firstelectric signal of the first frequency and the first detection signaland a first variable which is the square root of the first frequency;supplying a second electric signal at a second frequency different fromthe first frequency, to the integrated circuit; acquiring a seconddetection signal indicative of a change of an amount of heat generationdetected from the integrated circuit in response the second electricsignal; acquiring a second phase shift between the second electricsignal of the second frequency and the second detection signal and asecond variable which is the square root of the second frequency; andacquiring depth information, x, of the heat generation point indicatingthe depth of the heat generation point in the integrated circuit, on thebasis of a variation of the phase shift, dbx, between the first phaseshift and the second phase shift, and a variation of the variable,df^(1/2), between the first variable and the second variable using thefollowing equation:${\frac{dbx}{d\sqrt{f}} = {x\sqrt{\frac{\rho\; q\;\pi}{k}}}},$ wherein ρis the density of the integrated circuit material, q is the specificheat of the integrated circuit material, and κ is the heat transfercoefficient of the integrated circuit material.
 2. The method accordingto claim 1, wherein duty ratios of the first electric signal are set tobe equal to duty ratios of the second electric signal.
 3. An apparatusfor acquiring a depth of a heat generation point in an integratedcircuit, comprising: an electric signal supply unit configured to supplyan electric signal to the integrated circuit; a control unit configuredto control the electric signal supply unit so as to supply a firstelectric signal at a first frequency and a second electric signal at asecond frequency different from the first frequency, to the integratedcircuit; a detection unit configured to acquire a first detection signalindicative of a change of an amount of heat generation detected from theintegrated circuit in response to supply of the first electric signaland configured to acquire a second detection signal indicative of achange of an amount of heat generation detected from the integratedcircuit in response to supply of the second electric signal; a phaseshift detection unit configured to acquire a first phase shift betweenthe first electric signal and the first detection signal and a secondphase shift between the second electric signal and the second detectionsignal; and a calculation unit configured to acquire a first variablewhich is the square root of the first frequency and a second variablewhich is the square root of the second frequency and acquire depthinformation, x, of the heat generation point indicating the depth of theheat generation point in the integrated circuit, on the basis of avariation of the phase shift, dbx, between the first phase shift and thesecond phase shift, and a variation of the variable, df^(1/2), betweenthe first variable and the second variable using the following equation:${\frac{dbx}{d\sqrt{f}} = {x\sqrt{\frac{\rho\; q\;\pi}{k}}}},$ wherein ρis the density of the integrated circuit material, q is the specificheat of the integrated circuit material, and κ is the heat transfercoefficient of the integrated circuit material.
 4. A method foracquiring a depth of a heat generation point in an integrated circuit,comprising: supplying a plurality of electric signals to the integratedcircuit; acquiring a plurality of detection signals indicative of achange of an amount of heat generation detected from the integratedcircuit in response to the plurality of electric signals; acquiring aplurality of phase shifts between one of the plurality of electricsignals and one of the plurality of detection signals that correspondsto the on of the plurality electric signals and a plurality of variableswhich are values of the square root of the frequencies of the pluralityof electric signal; and acquiring depth information, x, of the heatgeneration point indicating the depth of the heat generation point inthe integrated circuit on the basis of a variation of a phase shift,dbx, against a first of the plurality of phase shifts and a second ofthe plurality of phase shifts, and a variation of the variable,df^(1/2), between the first of the plurality of variables and the secondof the plurality of variables using the following equation:${\frac{dbx}{d\sqrt{f}} = {x\sqrt{\frac{\rho\; q\;\pi}{k}}}},$ wherein ρis the density of the integrated circuit material, q is the specificheat of the integrated circuit material and κ is the heat transfercoefficient of the integrated circuit material.
 5. The method accordingto claim 1, wherein the first detection signal and the second detectionsignal are acquired on the basis of a plurality of heat generationimages which is acquired in time series by using an imaging device. 6.The method according to claim 5, wherein a frame rate of the imagingdevice is set on the basis of the first frequency or the secondfrequency.
 7. The method according to claim 1, wherein the firstfrequency and the second frequency are set to no more than 10 Hz.
 8. Themethod according to claim 1, wherein the first phase shift and thesecond phase shift are acquired by using a lock-in detector.
 9. Theapparatus according to claim 3, wherein duty ratios of the firstelectric signal are equal to duty ratios of the second electric signal.10. The apparatus according to claim 3, wherein the detection unitcomprises an imaging device configured to acquire in time series aplurality of heat generation images and configured to acquire the firstdetection signal and the second detection signal on the basis of theplurality of heat generation images.
 11. The apparatus according toclaim 10, wherein a frame rate of the imaging device is set on the basisof the first frequency or the second frequency.
 12. The apparatusaccording to claim 3, wherein the first frequency and the secondfrequency are set to no more than 10 Hz.
 13. The apparatus according toclaim 3, wherein the phase shift detection unit configured to detect thefirst phase shift and the second phase shift by lock-in detection. 14.An apparatus for acquiring a depth of a heat generation point in anintegrated circuit, comprising: an electric signal supply configured tosupply a plurality of electric signals to the integrated circuit; adetection unit configured to acquire a detection signal indicative of achange of an amount of heat generation detected from the integratedcircuit in response each of the electric signals; a phase shiftacquisition unit configured to acquire a phase shift between theelectric signal and the detection signal and a variable which is thesquare root of the frequency of the electric signal; and a calculationunit configured to acquire depth information of the heat generationpoint, x, indicating the depth of the heat generation point in theintegrated circuit, on the basis of a variation of the phase shift, dbx,between the first phase shift and the second phase shift, and avariation of the variable, df^(1/2), between the first variable and thesecond variable using the following equation:${\frac{dbx}{d\sqrt{f}} = {x\sqrt{\frac{\rho\; q\;\pi}{k}}}},$ wherein ρis the density of the integrated circuit material, q is the specificheat of the integrated circuit material, and κ is the heat transfercoefficient of the integrated circuit material.